QJEEM11Ph7497: JEE Main 2011 Physics - Class 11 JEEM11Ph7497 Solution: A mass M , attached to a horizontal spring, executes S . H . M…

Question

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A mass

M,

attached to a horizontal spring, executes

S . H . M .

with amplitude

A_{1} .

When the mass

M

passes through its mean position then a smaller mass

m

is placed over it and both of them move together with amplitude

A_{2} .

The ratio of

(\frac{A_{1}}{A_{2}})

is :

Accepted Answer

The net force becomes zero at the mean point. Therefore, linear momentum must be conserved.

∴

M v_{1} = (M + m) v_{2}

M A_{1} \sqrt{\frac{k}{M}} = (M + m) A_{2} \sqrt{\frac{k}{m + M}}

∴

(V = A \sqrt{\frac{k}{M}})

A_{1} \sqrt{M} = A_{2} \sqrt{M + m}

∴

\frac{A_{1}}{A_{2}} = \sqrt{\frac{m + M}{M}}

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